Autofocus for digital Fresnel holograms by use of a Fresnelet-sparsity criterion

We propose a robust autofocus method for reconstructing digital Fresnel holograms. The numerical reconstruction involves simulating the propagation of a complex wave front to the appropriate distance. Since the latter value is difficult to determine manually, it is desirable to rely on an automatic procedure for finding the optimal distance to achieve high-quality reconstructions. Our algorithm maximizes a sharpness metric related to the sparsity of the signal’s expansion in distance-dependent waveletlike Fresnelet bases. We show results from simulations and experimental situations that confirm its applicability

Semi-Blind Spatially-Variant Deconvolution in Optical Microscopy with Local Point Spread Function Estimation By Use Of Convolutional Neural Networks

We present a semi-blind, spatially-variant deconvolution technique aimed at optical microscopy that combines a local estimation step of the point spread function (PSF) and deconvolution using a spatially variant, regularized Richardson-Lucy algorithm. To find the local PSF map in a computationally tractable way, we train a convolutional neural network to perform regression of an optical parametric model on synthetically blurred image patches. We deconvolved both synthetic and experimentally-acquired data, and achieved an improvement of image SNR of 1.00 dB on average, compared to other deconvolution algorithms.Comment: 2018/02/11: submitted to IEEE ICIP 2018 - 2018/05/04: accepted to IEEE ICIP 201

Probing Near-Horizon Fluctuations with Black Hole Binary Mergers

The strong version of the nonviolent nonlocality proposal of Giddings predicts "strong but soft" quantum metric fluctuations near black hole horizons in an attempt to resolve the information paradox. To study observable signatures of this proposal, we numerically solve Einstein's equations modified by these fluctuations and analyze the gravitational wave signal from the inspiral and merger of two black holes. In a model of evolution for such fluctuations, we show that they lead to significant deviations in the observed waveform, even when the black holes are still well separated, and could potentially be observed by aLIGO.Comment: 7 pages, 6 figures; v2: published versio

DeepFocus: a Few-Shot Microscope Slide Auto-Focus using a Sample Invariant CNN-based Sharpness Function

Autofocus (AF) methods are extensively used in biomicroscopy, for example to acquire timelapses, where the imaged objects tend to drift out of focus. AD algorithms determine an optimal distance by which to move the sample back into the focal plane. Current hardware-based methods require modifying the microscope and image-based algorithms either rely on many images to converge to the sharpest position or need training data and models specific to each instrument and imaging configuration. Here we propose DeepFocus, an AF method we implemented as a Micro-Manager plugin, and characterize its Convolutional neural network-based sharpness function, which we observed to be depth co-variant and sample-invariant. Sample invariance allows our AF algorithm to converge to an optimal axial position within as few as three iterations using a model trained once for use with a wide range of optical microscopes and a single instrument-dependent calibration stack acquisition of a flat (but arbitrary) textured object. From experiments carried out both on synthetic and experimental data, we observed an average precision, given 3 measured images, of 0.30 +- 0.16 micrometers with a 10x, NA 0.3 objective. We foresee that this performance and low image number will help limit photodamage during acquisitions with light-sensitive samples.Comment: Submitted to IEEE ISBI 202

Free annotated data for deep learning in microscopy? A hitchhiker's guide

In microscopy, the time burden and cost of acquiring and annotating large datasets that many deep learning models take as a prerequisite, often appears to make these methods impractical. Can this requirement for annotated data be relaxed? Is it possible to borrow the knowledge gathered from datasets in other application fields and leverage it for microscopy? Here, we aim to provide an overview of methods that have recently emerged to successfully train learning-based methods in bio-microscopy.Comment: Accepted in Photoniques 10

On Fresnelets, interference fringes, and digital holography

In this thesis, we describe new approaches and methods for reconstructing complex-valued wave fields from digital holograms. We focus on Fresnel holograms recorded in an off-axis geometry, for which operational real-time acquisition setups readily exist. The three main research directions presented are the following. First, we derive the necessary tools to port methods and concepts of wavelet-based approaches to the field of digital holography. This is motivated by the flexibility, the robustness, and the unifying view that such multiresolution procedures have brought to many applications in image processing. In particular, we put emphasis on space-frequency processing and sparse signal representations. Second, we propose to decouple the demodulation from the propagation problem, which are both inherent to digital Fresnel holography. To this end, we derive a method for retrieving the amplitude and phase of the object wave through a local analysis of the hologram's interference fringes. Third, since digital holography reconstruction algorithms involve a number of parametric models, we propose automatic adjustment methods of the corresponding parameters. We start by investigating the Fresnel transform, which plays a central role in both the modeling of the acquisition procedure and the reconstruction of complex wave fields. The study of the properties that are central to wavelet and multiresolution analysis leads us to derive Fresnelets, a new family of wavelet-like bases. Fresnelets permit the analysis of holograms with a good localization in space and frequency, in a way similar to wavelets for images. Since the relevant information in a Fresnel off-axis hologram may be separated both in space and frequency, we propose an approach for selectively retrieving the information in the Fresnelet domain. We show that in certain situations, this approach is superior to others that exclusively rely on the separation in space or frequency. We then derive a least-squares method for the estimation of the object wave's amplitude and phase. The approach, which is reminiscent of phase-shifting techniques, is sufficiently general to be applied in a wide variety of situations, including those dictated by the use of microscopy objectives. Since it is difficult to determine the reconstruction distance manually, we propose an automatic procedure. We take advantage of our separate treatment of the phase retrieval and propagation problems to come up with an algorithm that maximizes a sharpness metric related to the sparsity of the signal's expansion in distance-dependent Fresnelet bases. Based on a simulation study, we suggest a number of guidelines for deciding which algorithm to apply to a given problem. We compare existing and the newly proposed solutions in a wide variety of situations. Our final conclusion is that the proposed methods result in flexible algorithms that are competitive with preexisting ones and superior to them in many cases. Overall, they may be applied in a wide range of experimental situations at a low computational cost

Discretization of the radon transform and of its inverse by spline convolutions

We present an explicit formula for B-spline convolution kernels; these are defined as the convolution of several B-splines of variable widths hi and degrees ni. We apply our results to derive spline-convolution-based algorithms for two closely related problems: the computation of the Radon transform and of its inverse. First, we present an efficient discrete implementation of the Radon transform that is optimal in the least-squares sense. We then consider the reverse problem and introduce a new spline-convolution version of the filtered back-projection algorithm for tomographic reconstruction. In both cases, our explicit kernel formula allows for the use of high-degree splines; these offer better approximation performance than the conventional lower-degree formulations (e.g., piecewise constant or piecewise linear models). We present multiple experiments to validate our approach and to find the parameters that give the best tradeoff between image quality and computational complexity. In particular, we find that it can be computationally more efficient to increase the approximation degree than to increase the sampling rate

Continuous wavelet transform ridge extraction for spectral interferometry imaging

The combination of wavelength multiplexing and spectral interferometry allows for the encoding of multidimensional information and its transmission over a mono-dimensional channel; for example, measurements of a surface's topography acquired through a monomode fiber in a small endoscope. The local depth of the imaged object is encoded in the local spatial frequency of the signal measured at the output of the fiber-decoder system. We propose a procedure to retrieve the depth-map by determining the signal's instantaneous frequency. First, we compute its continuous, complex-valued, wavelet transform (CWT). The frequency signature at every position is contained in the resulting scalogram. We then extract the ridge of maximal response by use of a dynamic programming algorithm thus directly recovering the object's topography. We present results that validate this procedure based on both simulated and experimental data

High-speed multicolor microscopy of repeating dynamic processes

Images of multiply labeled fluorescent samples provide unique insights into the localization of molecules, cells, and tissues. The ability to image multiple channels simultaneously at high speed without cross talk is limited to a few colors and requires dedicated multichannel or multispectral detection procedures. Simpler microscopes, in which each color is imaged sequentially, produce a much lower frame rate. Here, we describe a technique to image, at high frame rate, multiply labeled samples that have a repeating motion. We capture images in a single channel at a time over one full occurrence of the motion then repeat acquisition for other channels over subsequent occurrences. We finally build a high-speed multichannel image sequence by combining the images after applying a normalized mutual information-based time registration procedure. We show that this technique is amenable to image the beating heart of a double-labeled embryonic quail in three channels (brightfield, yellow, and mCherry fluorescent proteins) using a fluorescence wide-field microscope equipped with a single monochrome camera and without fast channel switching optics. We experimentally evaluate the accuracy of our method on image series from a two-channel confocal microscope